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Metric Space
★★★☆☆High School
📖Definition
A metric space is a set equipped with a distance function (metric) between points. It's a special case of topological spaces.
📐Formulas
d(x, y) ≥ 0, d(x,y) = 0 ⇔ x = y
Non-negativity and identity
d(x, y) = d(y, x)
Symmetry
d(x, z) ≤ d(x, y) + d(y, z)
Triangle inequality
✏️Examples
예제 1
Define Euclidean distance in ℝ².
예제 2
Define Manhattan (taxicab) distance.
⚡Applications
Analysis
Convergence, continuity, completeness
Machine Learning
Clustering, k-NN
Optimization
Distance-based algorithms
🔗Related Documents
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